Because Coretta lived through the 60s, 70s, 80s, 90s and 2000s to see the changes and her perception and opinion changed as well. But she's not the Reverend. MLK was. And his perception was based only up to the early 1960s.
And if hiss belief is strong as he was back then then certainly his belief would be just as strong today like her niece Alevda King.
Same sex marriage was a completely foreign if not taboo subject back in the 1950s and 1960s to most of the population. It's completely different today where people are exposed to that. Remember Prop 8 in California? Blacks are known to be socially conservative than not, especially on same sex marriage.
60% of blacks think it should be illegal to only 28% who think it should be allowed. Whites support same sex marriage by a 48/47 margin, Hispanics with47/41 and Asians at 52/38 in a poll survey.
http://www.publicpolicypolling.com/pdf/gaymarriagetoplines.pdf